In this paper, we investigate the performance of a distributed space-time coding based hybrid satellite- terrestrial cooperative network (DSTC-HSTCN), where both the satelliterelay and satellite-destination links undergo the Shadowed-Rician fading, whereas the relay-destination link follows the Rayleigh fading. In particular, we address the problem in a downlink distributed Alamouti coded satellite system with a single fixed terrestrial relay. By assuming that amplify-and-forward (AF) protocol is adopted at the terrestrial relay, we first derive the analytical expressions for the joint probability density function (PDF) and moment generating function (MGF) of the signal to noise ratio (SNR) for the cooperatively encoding phase. Then, based on the Meijer-G functions, we present an approximated yet accurate method to evaluate the outage probability and symbol error rate (SER) of the considered networks. Finally, Simulation results are provided to demonstrate the validity of the theoretical analysis.
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